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<a href="_k_means_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//===========================================================================</span><span class="comment"></span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> * </span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * \brief       The k-means clustering algorithm.</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * </span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * </span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> *</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * \author      T. Glasmachers</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * \date        2011</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> *</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * </span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * </span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * </span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * </span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> *</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> */</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="comment">//===========================================================================</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_KMEANS_H</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#define SHARK_ALGORITHMS_KMEANS_H</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="preprocessor">#include &lt;<a class="code" href="_d_l_l_support_8h.html">shark/Core/DLLSupport.h</a>&gt;</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#include &lt;<a class="code" href="_dataset_8h.html">shark/Data/Dataset.h</a>&gt;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="preprocessor">#include &lt;<a class="code" href="_centroids_8h.html">shark/Models/Clustering/Centroids.h</a>&gt;</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="preprocessor">#include &lt;<a class="code" href="_r_b_f_layer_8h.html">shark/Models/RBFLayer.h</a>&gt;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="preprocessor">#include &lt;<a class="code" href="_kernel_expansion_8h.html">shark/Models/Kernels/KernelExpansion.h</a>&gt;</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="preprocessor">#include &lt;<a class="code" href="_kernel_helpers_8h.html">shark/Models/Kernels/KernelHelpers.h</a>&gt;</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a>{</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment"></span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment">///</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment">/// \brief The k-means clustering algorithm.</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="comment">///</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment">/// \par</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="comment">/// The k-means algorithm takes vector-valued data</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment">/// \f$ \{x_1, \dots, x_n\} \subset \mathbb R^d \f$</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment">/// and splits it into k clusters, based on centroids</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">/// \f$ \{c_1, \dots, c_k\} \f$.</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">/// The result is stored in a Centroids object that can be used to</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">/// construct clustering models.</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">///</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment">/// \par</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment">/// This implementation starts the search with the given centroids,</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">/// in case the provided centroids object (third parameter) contains</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span><span class="comment">/// a set of k centroids. Otherwise the search starts from the first</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span><span class="comment">/// k data points.</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="comment">///</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="comment">/// \par</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span><span class="comment">/// Note that the data set needs to include at least k data points</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="comment">/// for k-means to work. This is because the current implementation</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span><span class="comment">/// does not allow for empty clusters.</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span><span class="comment">///</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="comment">/// \param data           vector-valued data to be clustered</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span><span class="comment">/// \param k              number of clusters</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span><span class="comment">/// \param centroids      centroids input/output</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span><span class="comment">/// \param maxIterations  maximum number of k-means iterations; 0: unlimited</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span><span class="comment">/// \return               number of k-means iterations</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><span class="comment">/// \ingroup clustering</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"><a class="line" href="group__clustering.html#ga18f3e34980a5e92ad240649988ac314c">   78</a></span><span class="comment"></span><a class="code hl_define" href="_d_l_l_support_8h.html#a54b73283f7f70b27fbd8ac5d4621827f" title="Defines SHARK_COMPILE_DLL.">SHARK_EXPORT_SYMBOL</a> std::size_t <a class="code hl_function" href="group__clustering.html#ga18f3e34980a5e92ad240649988ac314c" title="The k-means clustering algorithm.">kMeans</a>(<a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;RealVector&gt;</a> <span class="keyword">const</span>&amp; data, std::size_t k, <a class="code hl_class" href="classshark_1_1_centroids.html" title="Clusters defined by centroids.">Centroids</a>&amp; centroids, std::size_t maxIterations = 0);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="comment"></span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span><span class="comment">///</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span><span class="comment">/// \brief The k-means clustering algorithm for initializing an RBF Layer</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span><span class="comment">///</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span><span class="comment">/// \par</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span><span class="comment">/// The k-means algorithm takes vector-valued data</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment">/// \f$ \{x_1, \dots, x_n\} \subset \mathbb R^d \f$</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span><span class="comment">/// and splits it into k clusters, based on centroids</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span><span class="comment">/// \f$ \{c_1, \dots, c_k\} \f$.</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="comment">/// The result is stored in a RBFLayer object that can be used to</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="comment">/// construct clustering models.</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span><span class="comment">///</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span><span class="comment">/// \par</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span><span class="comment">/// This is just an alternative frontend to the version using Centroids. it creates a centroid object,</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span><span class="comment">///  with as many clusters as are outputs in the RBFLayer and copies the result into the model.</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span><span class="comment">///</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span><span class="comment">/// \par</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span><span class="comment">/// Note that the data set needs to include at least k data points</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span><span class="comment">/// for k-means to work. This is because the current implementation</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span><span class="comment">/// does not allow for empty clusters.</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span><span class="comment">///</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span><span class="comment">/// \param data           vector-valued data to be clustered</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span><span class="comment">/// \param model     RBFLayer input/output</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span><span class="comment">/// \param maxIterations  maximum number of k-means iterations; 0: unlimited</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span><span class="comment">/// \return               number of k-means iterations</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span><span class="comment">///</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"><a class="line" href="namespaceshark.html#aac4a76067e70f1148562d9ade589e04c">  105</a></span><span class="comment"></span><a class="code hl_define" href="_d_l_l_support_8h.html#a54b73283f7f70b27fbd8ac5d4621827f" title="Defines SHARK_COMPILE_DLL.">SHARK_EXPORT_SYMBOL</a> std::size_t <a class="code hl_function" href="group__clustering.html#ga18f3e34980a5e92ad240649988ac314c" title="The k-means clustering algorithm.">kMeans</a>(<a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;RealVector&gt;</a> <span class="keyword">const</span>&amp; data, <a class="code hl_class" href="classshark_1_1_r_b_f_layer.html" title="Implements a layer of radial basis functions in a neural network.">RBFLayer</a>&amp; model, std::size_t maxIterations = 0);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span><span class="comment"></span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span><span class="comment">///</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span><span class="comment">/// \brief The kernel k-means clustering algorithm</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span><span class="comment">///</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span><span class="comment">/// \par</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span><span class="comment">/// The kernel k-means algorithm takes data</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="comment">/// \f$ \{x_1, \dots, x_n\} \f$</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span><span class="comment">/// and splits it into k clusters, based on centroids</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span><span class="comment">/// \f$ \{c_1, \dots, c_k\} \f$.</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span><span class="comment">/// The centroids are elements of the reproducing kernel Hilbert space</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span><span class="comment">/// (RHKS) induced by the kernel function. They are functions, represented</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span><span class="comment">/// as the components of a KernelExpansion object. I.e., given a data point</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span><span class="comment">/// x, the kernel expansion returns a k-dimensional vector f(x), which is</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span><span class="comment">/// the evaluation of the centroid functions on x. The value of the</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span><span class="comment">/// centroid function represents the inner product of the centroid with</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span><span class="comment">/// the kernel-induced feature vector of x (embedding of x into the RKHS).</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span><span class="comment">/// The distance of x from the centroid \f$ c_i \f$ is computes as the</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span><span class="comment">/// kernel-induced distance</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="comment">/// \f$ \sqrt{ kernel(x, x) + kernel(c_i, c_i) - 2 kernel(x, c_i) } \f$.</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span><span class="comment">/// For the Gaussian kernel (and other normalized kernels) is simplifies to</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span><span class="comment">/// \f$ \sqrt{ 2 - 2 kernel(x, c_i) } \f$. Hence, larger function values</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span><span class="comment">/// indicate smaller distance to the centroid.</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span><span class="comment">///</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span><span class="comment">/// \par</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span><span class="comment">/// Note that the data set needs to include at least k data points</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span><span class="comment">/// for k-means to work. This is because the current implementation</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span><span class="comment">/// does not allow for empty clusters.</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span><span class="comment">///</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span><span class="comment">/// \param dataset        vector-valued data to be clustered</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span><span class="comment">/// \param k              number of clusters</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span><span class="comment">/// \param kernel         kernel function object</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span><span class="comment">/// \param maxIterations  maximum number of k-means iterations; 0: unlimited</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="comment">/// \return               centroids (represented as functions, see description)</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span><span class="comment">///</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span><span class="comment"></span><span class="keyword">template</span>&lt;<span class="keyword">class</span> InputType&gt;</div>
<div class="foldopen" id="foldopen00141" data-start="{" data-end="}">
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"><a class="line" href="namespaceshark.html#a568356ff4d6d42f5c11402e9cac7d8aa">  141</a></span><a class="code hl_class" href="classshark_1_1_kernel_expansion.html" title="Linear model in a kernel feature space.">KernelExpansion&lt;InputType&gt;</a> <a class="code hl_function" href="group__clustering.html#ga18f3e34980a5e92ad240649988ac314c" title="The k-means clustering algorithm.">kMeans</a>(<a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;InputType&gt;</a> <span class="keyword">const</span>&amp; dataset, std::size_t k, <a class="code hl_class" href="classshark_1_1_abstract_kernel_function.html" title="Base class of all Kernel functions.">AbstractKernelFunction&lt;InputType&gt;</a>&amp; kernel, std::size_t maxIterations = 0){</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <span class="keywordflow">if</span>(!maxIterations)</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        maxIterations = std::numeric_limits&lt;std::size_t&gt;::max();</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    </div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    std::size_t n = dataset.<a class="code hl_function" href="group__shark__globals.html#ga814e8b0028cc90dd2af69805e8f8a04d" title="Returns the total number of elements.">numberOfElements</a>();</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>    RealMatrix kernelMatrix = <a class="code hl_function" href="group__kernels.html#ga3eaca71bfc1467b79c9341dcfcad25c1" title="Calculates the regularized kernel gram matrix of the points stored inside a dataset.">calculateRegularizedKernelMatrix</a>(kernel,dataset,0);</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    UIntVector clusterMembership(n);</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    UIntVector clusterSizes(k,0);</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>    RealVector ckck(k,0);</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    </div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <span class="comment">//init cluster assignments</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>    <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i != n; ++i){</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        clusterMembership(i) = i % k;</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    }</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    std::shuffle(clusterMembership.begin(),clusterMembership.end(),<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>);</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <span class="keywordflow">for</span>(std::size_t i = 0; i != n; ++i){</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        ++clusterSizes(clusterMembership(i));</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    }</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    </div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    <span class="comment">// k-means loop</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    std::size_t iter = 0;</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    <span class="keywordtype">bool</span> equal = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    <span class="keywordflow">for</span>(; iter != maxIterations &amp;&amp; !equal; ++iter) {</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        <span class="comment">//the clustering model results in centers c_k= 1/n_k sum_i k(x_i,.) for all x_i points of cluster k</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        <span class="comment">//we need to compute the squared distances between all centers and points that is</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        <span class="comment">//d^2(c_k,x_i) = &lt;c_k,c_k&gt; -2 &lt; c_k,x_i&gt; + &lt;x_i,x_i&gt; for the i-th point.</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        <span class="comment">//thus we precompute &lt;c_k,c_k&gt;= sum_ij k(x_i,x_j)/(n_k)^2 for all x_i,x_j points of cluster k</span></div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        ckck.clear();</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != n; ++i){</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>            std::size_t c1 = clusterMembership(i);</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>            <span class="keywordflow">for</span>(std::size_t j = 0; j != n; ++j){</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>                std::size_t c2 = clusterMembership(j);</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>                <span class="keywordflow">if</span>(c1 != c2) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>                ckck(c1) += kernelMatrix(i,j);</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            }</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        }</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        noalias(ckck) = safe_div(ckck,<a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>(clusterSizes),0);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span> </div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        UIntVector newClusterMembership(n);</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        RealVector currentDistances(k);</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != n; ++i){</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>            <span class="comment">//compute squared distances between the i-th point and the centers</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>            <span class="comment">//we skip &lt;x_i,x_i&gt; as it is always the same for all elements and we don&#39;t need it for comparison</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>            noalias(currentDistances) = ckck;</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>            <span class="keywordflow">for</span>(std::size_t j = 0; j != n; ++j){</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                std::size_t c = clusterMembership(j);</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>                currentDistances(c) -= 2* kernelMatrix(i,j)/clusterSizes(c);</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>            }</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>            <span class="comment">//choose the index with the smallest distance as new cluster</span></div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>            newClusterMembership(i) = (<span class="keywordtype">unsigned</span> int) arg_min(currentDistances);</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        }</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        equal = boost::equal(</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>            newClusterMembership,</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            clusterMembership</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        );</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        noalias(clusterMembership) = newClusterMembership;</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        <span class="comment">//compute new sizes of clusters</span></div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        clusterSizes.clear();</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != n; ++i){</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>            ++clusterSizes(clusterMembership(i));</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        }</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span> </div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        <span class="comment">//if a cluster is empty then assign a random point to it</span></div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i != k; ++i){</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>            <span class="keywordflow">if</span>(clusterSizes(i) == 0){</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>                std::size_t elem = <a class="code hl_function" href="namespaceshark_1_1random.html#a18f302ea18f70835c59935973ba8ea84" title="Draws a number uniformly in [lower,upper] by drawing random numbers from rng.">random::uni</a>(<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>, std::size_t(0), n-1);</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>                --clusterSizes(clusterMembership(elem));</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>                clusterMembership(elem)=i;</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>                clusterSizes(i) = 1;</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>            }</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>        }</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    }</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    </div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <span class="comment">//copy result in the expansion</span></div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    <a class="code hl_class" href="classshark_1_1_kernel_expansion.html" title="Linear model in a kernel feature space.">KernelExpansion&lt;InputType&gt;</a> expansion;</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    expansion.<a class="code hl_function" href="classshark_1_1_kernel_expansion.html#a38c97766f52bf00e5b0120c46c15f37f">setStructure</a>(&amp;kernel,dataset,<span class="keyword">true</span>,k);</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    expansion.<a class="code hl_function" href="classshark_1_1_kernel_expansion.html#a1c89cb50933ee211d67af90e6366e0ee">offset</a>() = -ckck;</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    expansion.<a class="code hl_function" href="classshark_1_1_kernel_expansion.html#a3c65dfd17f38eaa461f6400d302fae48">alpha</a>().clear();</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    <span class="keywordflow">for</span>(std::size_t i = 0; i != n; ++i){</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        std::size_t c = clusterMembership(i);</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>        expansion.<a class="code hl_function" href="classshark_1_1_kernel_expansion.html#a3c65dfd17f38eaa461f6400d302fae48">alpha</a>()(i,c) = 2.0 / clusterSizes(c);</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    }</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span> </div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <span class="keywordflow">return</span> expansion;</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>}</div>
</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span> </div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>} <span class="comment">// namespace shark</span></div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span><span class="preprocessor">#endif</span></div>
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